Local-Nonequilibrium Solidification Model (LNSM) has been introduced for interpretation of phenomena in rapid solidification. Modern experimental techniques and advanced technologies of melting and solidification of metallic and non-metallic systems allow us to reach deep undercoolings, large temperature and concentration gradients, and high velocities of the phase transformations. E.g., in modern experiments the interface velocity reaches 10-100 m/s and the liquid phase can be undercooled in a wide range of 10 to 400 K. Reaching such deep undercoolings leads to large gradients of Gibbs free energy which are considered as a driving force of phase transformations in rapid solidification.
For large driving forces and with increasing velocity of the phase transformation, the solute diffusion field near the rapidly propagating solidification front has no time to completely relax to local thermodynamic equilibrium. A deviation from local thermodynamic equilibrium occurs both in bulk phases and at the interface. As a result, nonequilibrium effects (such as solute trapping, disorder trapping, and solute drag) play a crucial role in formation of metastable or nonequilibrium phases and structures.
At extreme undercooling values, the crystals begin to grow with the initial chemical composition of the liquid in a segregation-free growth mode. In such a case, interface moves with the velocity greater than the solute diffusion speed in bulk phases. This growth mode proceeds by the diffusionless mechanism which occurs in association with morphological transformations of patterns. To describe these effects, LNSM is suggested as a useful theoretical and computational tool for description of pattern formation evolving far from thermodynamic equilibrium.